Thank you for another well-considered article, Michael!
To me, the approach of secondary reinforcer and variable rewards seems quite intuitive. I've used this approach with my budgie at times and it works a treat. It's certainly not changed the effectiveness of the clicker at all. I use it for repetitive iterations of a trick - flight recalls and targeting (variable), putting multiple items in a container etc.
Karen Pryor's FAQ on clicker training says:
Do clickers and treats need to be used for every behavior, forever?
No. Once a behavior is learned and on cue, there’s usually no need to click, as the animal understands the behavior. Clicker trainers can maintain the behavior by replacing specially good treats with occasional and less intensive rewards including a pat or praise. Learned cues and behaviors are also maintained by real-life rewards: for example sitting quietly at the door is rewarded by opening the door so that the dog can have a walk. Clicker trainers then save clicks and treats for the next new thing they want to train.
Even when I don't explicitly reward, the click and the attention that goes with it must let Wiki feel rewarded enough to continue, and that's the purpose of the reward. I think our training buddies enjoy the interaction and attention and challenge, and that's partly their "real-life reward". We practice without a clicker on occasion, too - it's how I know whether he really enjoys doing something or not!
I think we shouldn't underestimate the capacity for understanding in our birds, and their ability to give a more subtle meaning to the clicker than just a 1:1 relationship of "click = food". There are many "old school" trainers who work with multiple performing birds and do not use clickers or even rewards when performing (yes, I even get given a hard time by them for "needing" a clicker in the first place), so I don't think we should be too precious about what is in essence a communication tool.